def 							UpperCamelCase		(			__lowercase		:					list[int]		,__lowercase		:					list[int]      ):
		'''simple docstring'''




		if not len(__lowercase      ) == len(__lowercase      ) == 3:
				raise ValueError('Please enter a valid equation.'      )
		if equationa[0] == equationa[1] == equationa[0] == equationa[1] == 0:
				raise ValueError('Both a & b of two equations can\'t be zero.'      )

		# Extract the coefficients
		A_  ,     A_  ,     A_						:							List[str]      = equationa
		A_  ,     A_  ,     A_						:							Any      = equationa

		# Calculate the determinants of the matrices
		A_						:							int      = aa * ba - aa * ba
		A_						:							int      = ca * ba - ca * ba
		A_						:							Any      = aa * ca - aa * ca

		# Check if the system of linear equations has a solution (using Cramer's rule)
		if determinant == 0:
				if determinant_x == determinant_y == 0:
						raise ValueError('Infinite solutions. (Consistent system)'      )
				else:
						raise ValueError('No solution. (Inconsistent system)'      )
		else:
				if determinant_x == determinant_y == 0:
						# Trivial solution (Inconsistent system)
						return (0.0, 0.0)
				else:
						A_						:							str      = determinant_x / determinant
						A_						:							str      = determinant_y / determinant
						# Non-Trivial Solution (Consistent system)
						return (x, y)







import sys
import turtle




def 							UpperCamelCase		(			__lowercase		:					tuple[float, float]		,__lowercase		:					tuple[float, float]      ):
		'''simple docstring'''




		return (pa[0] + pa[0]) / 2, (pa[1] + pa[1]) / 2




def 							UpperCamelCase		(			__lowercase		:					tuple[float, float]		,__lowercase		:					tuple[float, float]		,__lowercase		:					tuple[float, float]		,__lowercase		:					int		,):
		'''simple docstring'''




		my_pen.up()
		my_pen.goto(vertexa[0]		,vertexa[1]      )
		my_pen.down()
		my_pen.goto(vertexa[0]		,vertexa[1]      )
		my_pen.goto(vertexa[0]		,vertexa[1]      )
		my_pen.goto(vertexa[0]		,vertexa[1]      )

		if depth == 0:
				return

		triangle(__lowercase		,get_mid(__lowercase		,__lowercase      )		,get_mid(__lowercase		,__lowercase      )		,depth - 1      )
		triangle(__lowercase		,get_mid(__lowercase		,__lowercase      )		,get_mid(__lowercase		,__lowercase      )		,depth - 1      )
		triangle(__lowercase		,get_mid(__lowercase		,__lowercase      )		,get_mid(__lowercase		,__lowercase      )		,depth - 1      )


if __name__ == "__main__":
	if len(sys.argv) != 2:
		raise ValueError(
		    """Correct format for using this script: """
		    """python fractals.py <int:depth_for_fractal>"""
		)
	_UpperCAmelCase          =						turtle.Turtle()
	my_pen.ht()
	my_pen.speed(5)
	my_pen.pencolor("""red""")

	_UpperCAmelCase          =						[(-175, -125), (0, 175), (175, -125)]  # vertices of triangle
	triangle(vertices[0], vertices[1], vertices[2], int(sys.argv[1]))






